CN101033748B - Method for determining pump flow without the use of traditional sensors - Google Patents

Abstract

A method of determining pump flow without the use of conventional sensors, comprising the steps of: creating a calibrated power curve at several rotational speeds at valve-closed conditions; Calculation coefficients; and used to solve polynomial power equations for flow at the current operating point. A calibrated power curve may be created by increasing the speed of the pump from a minimum speed to a maximum speed while operating the pump with the bleed valve closed. This data is used to correct the published performance of shut-off power at rated speed and best efficiency point power to determine the power ratio of the pump. It is also used to accurately determine the valve closing power at the current operating speed. A polynomial power equation may include, for example, a third order polynomial equation formed using coefficients from a normalized power versus flow curve, and corrections may be made for rotational speed, hydraulic efficiency, and specific gravity within the polynomial power equation.

Description

Method of Determining Pump Flow Without Using Traditional Sensors

Cross References to Related Applications

This patent application claims to enjoy the rights and interests of provisional patent application No.60/780,546 entitled "Method for Determining Pump Flow Without the Use of Traditional Sensors" (911-2.24-1/05GI003) filed on March 8, 2006. This patent Application also relates to Patent Application No. 11/601,373, filed November 17, 2006, entitled "Method and Apparatus For Pump Protection Without the Use of Traditional Sensors" (911-2.22-1/05GI002), and also to the March 2006 Provisional patent application No.60/780,547 entitled "Method for Optimizing ValvePosition and Pump Speed in a PID Control Valve System without the Use of External Sensors)" (911-2.23-1/06GI001) submitted on the 8th. The entire contents of all of these patent applications are hereby incorporated by reference.

technical field

The present invention relates to pump systems having pumps including centrifugal pumps; and in particular to methods of determining pump flow without the use of conventional sensors.

Background technique

Pumping devices are known in the art, the technologies associated with them and their disadvantages are as follows:

Pump controllers are known to apply the Pump Affinity Laws, which are approximations of how speed and impeller adjustments affect the performance (flow, head, power) of a centrifugal pump. While the laws of cutting are valid for general estimation, the factoring of power often results in over or underestimations of power based on the operating speed, size and specific speed of the pump. This error directly affects the algorithms for pump protection and flow prediction that may reside within programmable logic controllers (PLCs), distributed control systems (DCS), and variable frequency drives (VFDs).

Furthermore, deviations between actual pump performance and standard performance curves significantly reduce the accuracy of flow and/or pump condition estimates when pump performance mapping is established. The most common solution to this is to perform a pump performance test at multiple speeds to confirm precise pump performance. However, this solution can be timely, specialized and costly. In view of this situation, there is a need in the industry for a technique that can overcome the error of cutting laws.

U.S. Patent No. 6,715,996 B2 to Moeller discloses a method of operating a centrifugal pump by sampling the pump power at two rotational speeds with the valve closed, determining parasitic losses, and calculating Adjust power on to determine if the pump is operating with the valve closed. However, the method of correcting power under valve closed conditions like this starts to lose accuracy when the motor speed is below 50% of the rated speed, thus limiting the scope of application. This method of interpolating between power values at other speeds is partly based on cutting laws and is therefore not precise enough.

PCT WO2005/064167A1 to Witzel, Rolf et al. discloses a technique using calibrated power/differential pressure versus flow versus rotational speed curves. Calibrated data is stored and compared to current values to determine pump flow. This technique requires a differential pressure transmitter and requires a calibration curve of power/differential pressure versus flow to be stored in the evaluation device. This method is specific to obtaining traffic, thus reducing flexibility during field setup. It is also not easy to adjust to compensate for wear.

U.S. Patent No. 6,591,697 to Henyan discloses a method of determining the flow rate of a pump using motor torque measurements, which illustrates the relationship of torque and speed to pump flow rate and the use of a variable frequency drive (VFD) to adjust the speed of a centrifugal pump to regulate pump flow. ability. However, this technique utilizes flow versus torque curves calibrated for several dedicated rotational speeds, thus reducing flexibility during field setup. It is also not easily adjusted to compensate for wear.

US Patent No. 6,464,464 B2 to Sabini et al. discloses an apparatus and method for controlling a pump system based on a control and pump protection algorithm using a VFD to adjust the flow, pressure or speed of a centrifugal pump. However, this technique requires the use of auxiliary gauges, which increases the cost and complexity of the drive system, and adds possible points of failure and unnecessary cost. It also utilizes flow versus TDH curves calibrated at several dedicated speeds, thus reducing flexibility during field setup.

In addition, the following patents were found in the patentability search for the present invention. A summary of these patents is as follows.

Patent No. 4,358,821 discloses a method and apparatus for incorporating variable flow in process volume control, wherein the flow through is measured and the amount of material flowing through the process is determined by integrating the measurements.

Patent No. 5,213,477 discloses an apparatus for pump delivery flow rate control in which the maximum allowable flow rate is determined based on the relationship between available and desired net positive suction head (NPSH).

Patent No. 6,424,873 discloses a method and system for limiting the integral calculation components within a PID controller based on techniques that do not include the integral calculation components of the master PID controller or include only a portion thereof in the PID calculation.

Patent No. 6,546,295 discloses a method of tuning a process control loop in an industrial process in which field devices and process controllers are fine-tuned by determining control parameters of interacting controllers to provide desired process variability.

Patent No. 6,554,198 discloses a technique for controlling slope predictive control of a VAV box within a pressure-independent variable air volume (VAV) temperature control system based on a technique involving calculating the error between the airflow setpoint and the measured airflow and digital PID control.

Patent Publication No. 2004/0267395 discloses a system and method for dynamic multi-objective optimization of machine selection, integration and usage based on techniques in which diagnostic and machine data analyzed are based on A function that modifies resource utilization within an industrial automation system.

Patent Publication No. 2005/0237021 discloses a method and apparatus for pumping fluid at a constant average flow rate in a rotary drive apparatus of a construction machine.

None of the patents or publications mentioned above suggest or suggest techniques for determining pump flow without the use of conventional sensors as described herein.

Contents of the invention

The present invention provides a novel and unique method of determining pump flow in a centrifugal pump, centrifugal mixer, centrifugal blower or centrifugal compressor without using conventional sensors, the characteristic steps of which method are: creating A calibrated power curve for the conditions of the pump; coefficients are calculated from the power versus flow curve according to the power ratio of the pump; and the power equation is solved for the flow at the current operating point.

A calibrated power curve may be created by increasing the speed of the pump from a minimum speed to a maximum speed and collecting speed and power data at several speeds while operating the pump with the bleed valve closed. This data is used to correct the published performance at rated speed for shut-off power and best efficiency point power to determine the power ratio of the pump. It is also used to accurately determine the valve closing power at the current operating speed. This is necessary because published performance data often differ from actual data due to seal loss, wear, casting deviations, etc.

The power ratio of the pump is calculated by the following formula:

P _ratio =P _shutdown100% /P _{BEP_corr} .

The power equation may include, for example, a third order polynomial equation formed using coefficients from the normalized power versus flow curve, and corrections may be made for rotational speed and hydraulic efficiency within the polynomial power equation. In addition, complex roots can be determined to solve a third order polynomial equation with Muller's method or some other suitable method, and the calculated actual flow at a particular operating point can be determined.

The various steps of this method can be performed on a variable frequency drive (VFD) and a programmable logic controller (PLC) with one or more modules implementing the functions presented herein.

The present invention may also include a controller having one or more modules configured to perform the functions set forth herein and a pump system having such a controller.

Description of drawings

This specification includes the following drawings, in which:

Figure 1 is a block diagram of a basic pump system according to the present invention;

Figure 2 is a flowchart of the basic steps performed by the controller shown in Figure 1 in accordance with the present invention;

FIG. 3 is a block diagram of a controller shown in FIG. 1 for performing the basic steps shown in FIG. 2;

Figure 4 is a graph of % error (HP) versus rotational speed (RPM) using various methods such as cubic interpolation, method X, and cut law;

Figure 5 is a graph of power (HP) versus rotational speed (RPM) for actual drive power, tuned power, and cutting method with the valve closed;

Figure 6 is a graph of power (BHP) versus flow rate (GPM) for actual drive power, where the published pricebook (with seal) data and polynomial curve fit are also shown for each data set The tuning power correction data;

Figure 7 is a normalized graph of % Power (HP) versus % Flow (RPM) at RPMs of 1700, 2200, 2800, 3570, actual and as calculated; and

8 is a graph of tuned power (BHP) versus flow rate (GPM) for actual flow and calculated flow.

specific embodiment

FIG. 1 shows a basic pump system according to the invention, generally indicated at 2 , with a controller 4 , a motor 6 and a pump 8 . In operation, according to the present invention, the controller 4 is used to determine pump flow without the use of conventional sensors based on a technique consistent with that shown and described herein, wherein the technique creates Calibrate the power curve at the valve closed condition; calculate coefficients from the power versus flow curve based on the power ratio of the pump; and solve the power equation for the flow at the current operating point.

Figure 2 shows by way of example a flow chart generally indicated at 10 with the basic steps 10a, 10b, 10c of a pump flow determination algorithm that can be implemented by the controller 4 according to the invention. The determined flow value can also be used as an input to a PID control loop to control the flow without the need for an external flow meter or traditional measuring instrumentation. The flow determination algorithm may be embedded in a variable frequency drive or programmable logic controller, as described above for controller 4 in FIG. 1 .

According to the invention, a calibrated power curve can be created by increasing the speed of the pump from a minimum speed to a maximum speed while operating the pump with the discharge valve closed. This data is used to correct the published performance of shut-off power at rated speed and power at best efficiency point to determine the power ratio of the pump. It is also used to precisely determine the valve closing power at the current operating speed.

The power ratio of the pump can be calculated with the following formula:

P _ratio ＝P _shutdown100% /P _{BEP_corr} .

The power equation may include, for example, a third order polynomial equation formed using coefficients from the normalized power versus flow curve, some corrections may be made for rotational speed and hydraulic efficiency within the polynomial power equation. Furthermore, complex roots can be determined to solve this third order polynomial equation with Muller's method or some other suitable method so that the calculated actual flow at a particular operating point can be determined.

An advantage of the present invention is that the error of the cutting law is overcome by sampling the power at each rotational speed under the valve closed condition, so that an accurate power curve under the closed condition can be generated. By using a unique cubic interpolation method, pump power at valve closed conditions can be accurately determined over a wide range of rates. See the curves shown in Figures 4 and 5.

Power using published pump performance curve data will often differ from actual power due to linearly varying pump seal losses. The difference between the actual power at off condition and the published power can be used to bias (adjust) the power of the published curve at the best efficiency point (BEP) of the pump, since seal losses are constant for a given rotational speed . This approach eliminates the need for highly accurate pump performance curves (eg, factory testing) or more complex on-site calibration procedures. This process creates more accurate estimates of P _BEP and P _SO at different rotational speeds. This data can then be used to perform more advanced modeling of pump performance with minimal external data.

The method of integrating the normalized power coefficient within the third-order power equation eliminates the need to perform flow calibrations for parameters such as torque, power, or pressure at different speeds, eliminates the need for external transmitters, and provides Application flexibility during field setup. The present invention can provide wear compensation by periodically performing the tuning described in step A below.

Figure 3: Controller 4

FIG. 3 shows the basic modules 4 a , 4 b , 4 c , 4 d of the controller 4 . Many different types and types of controllers and control modules are known in the art that can be used to control pumps. Based on knowledge of such known controllers and control modules, in accordance with the present invention, one skilled in the art will be able to implement control modules such as 4a, 4b, 4c and configure them to perform in accordance with what is described herein functions, including: creating calibrated power curves at several speeds at valve-closed conditions; calculating normalized power curve coefficients from pump power ratios; and solving polynomial power equations for flow at the current operating point, such as in Fig. 2 and as explained above. For example, the functions of the modules 4a, 4b, 4c may be realized by hardware, software, firmware or a combination thereof, although the scope of the present invention is not limited to any specific embodiment of the present invention. In a typical software implementation, such a module would be one or more microprocessor-based CPUs with microprocessors, random access memory (RAM), read-only memory (ROM), input/output devices, and Architecture of control, data, and address buses. One skilled in the art does not require undue experience to program such a microprocessor-based implementation to perform the functions described herein. The scope of the invention is not limited to any particular embodiment using known or later developed technology.

The controller also has other controller modules 4d known in the art, these modules do not form an essential part of the invention and therefore they will not be described in detail here.

motor 6 and pump 8

The motor 6 and the pump 8 are well known in the art and will not be described in detail here. Furthermore, the scope of the present invention is not limited to any particular type or kind of motors and pumps now known or later developed. Furthermore, the scope of the present invention shall also include the use of techniques related to controlling the operation of centrifugal pumps, centrifugal agitators, centrifugal blowers or centrifugal compressors according to the present invention.

Method to realize

This flow calculation method has two basic steps:

Step A is to create a calibrated power curve at several rotational speeds at valve closed conditions.

Step B is calculating the normalized power curve coefficients based on the power ratio of the pump and solving the third order polynomial power equation for the flow at the current operating point.

Step A:

The logic according to the present invention is such that the speed of the pump is increased from a predetermined minimum speed (eg 30% of maximum speed) to a higher speed (eg 60% of maximum speed) when the pump is operated with the discharge valve closed. The speed ratio should be around 2:1. Power is then measured at these speeds and at 100% of the highest speed and corrected for specific gravity=1.

The shutdown power at any speed can then be determined using a unique cubic interpolation method:

The coefficients A-F are calculated as follows:

A＝(P _{SO_30％} )/(N _30％ )

B=(P _{SO_60%} -P _{SO_30%} )/(N _60% -N _30% )

C=(BA)/(N _60% -N _30% )

D=(P _{SO_100%} -P _{SO_60%} )/(N _100% -N _60% )

E＝(DB)/(N _100％ -N _30％ )

F＝(EC)/(N _100％ )

The shutdown power at any RPM is calculated as follows:

P _{SO_N} ＝A(N _ACT) +C(N _ACT )(N _ACT -N _30％ )+F(N _ACT )(N _ACT -N _30％ )(N _ACT -N _60％ ),

in:

P _{SO_30%} = P _{Meas_30%} / SG is the power measured at 30% of the rated motor speed corrected by specific gravity = 1,

P _{SO_60%} = P _{Meas_60%} / SG is the power measured at 60% of the rated motor speed corrected for specific gravity = 1, and

P _{SO — 100%} = P _{Meas — 100%} /SG is the power measured at 100% of the rated motor speed, corrected for specific gravity=1.

It is noted that for some embodiments, such as sealless pumps, the eddy current loss estimate must be subtracted from the measured shutoff power value.

It should also be noted that for some embodiments, such as small hp pumps acting on liquids with a specific gravity other than 1.0, mechanical losses (MechLoss) (such as seals and bearings) can be compensated for in the above shutdown power equation as follows:

P _{SO_N} = [(P _{Meas_N} -(Mech Loss x N _ACT /N _Rated ))/SG]+(Mech Loss x N _ACT /N _Rated ),

in

SG = specific gravity,

N _30% = 30% of the rated speed of the motor,

N _60% = the speed of 60% of the rated speed of the motor, and

N _100% = the rotational speed of 100% of the rated rotational speed of the motor.

Figure 5 is a graph showing the tuned power versus speed curve compared to the cut law power correction versus actual power at the valve closed (closed) condition.

In higher powered pumps, the speed must be limited during tuning to prevent the pump from overheating. In this case, the power at 100% RPM can be calculated with the following formula:

P _{SO_100%} = (N _100% /N _60% ) ^KSO x P _{SO_60%} ,

Among them, KSO is the closing index, with a typical value of 3.0.

The last step in the logic according to the invention is to estimate the power at the best efficiency point (BEP). This function relies on the observation that while the actual values of P _{BEP and} P _SO for any given pump may deviate significantly from the published performance curves, the slope of the power curve remains relatively constant.

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; BEP</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; corr</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{{\mathrm{<span\; class="notranslate">\; SO</span>}}_{\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \%</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; SO</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; BEP</span>}}$

in:

P _sO = pump power at off condition at 100% speed from published curves, and

P _BEP = pump power at BEP at 100% rotational speed from published curves.

Figure 6 is a graph showing the relationship of tuned power versus flow versus published bid curves. Note that the slopes of the two curves are the same.

Other less precise approximations can also be used to obtain the factor coefficient "K _SO ", which can be estimated by taking the ratio of the natural logarithm of the power ratio to the natural logarithm of the speed ratio as follows:

KSO＝LN(P _so1 /P _so2 )/LN(N ₁ /N ₂ )

in:

P _so1 = measured off power at speed N1, and

P _so2 = Measured off power at rotational speed N2.

The shutdown power at any speed can then be determined as:

P _{SO xrpm} ＝P _{SO yrpm} x(N _xrpm /N _yrpm ) ^KSO

in:

P _{SO xrpm} = off power at N _xrpm , and

P _{SO yrpm} = Off power at N _yrpm .

Step B:

To determine the calculated flow value, a normalized power curve is calculated from the power ratio of the pump, where:

P _Ratio ＝P _{SO_100%} /P _{BEP_corr} .

The normalization curve is specific to the power ratio and specific speed of the pump. The specific speed is a value related to the hydraulic performance of the centrifugal pump.

FIG. 7 shows by way of example a graph of normalized curves plotted for several rotational speeds for a 2x3-13 end suction pump with P _Ratio =0.45 and a specific rotational speed of 836 .

The table below shows the actual versus normalized test data for the flow and power of the 2x3-13 pump at 3570 rpm.

Flow (Gpm) normalized traffic Power (HP) normalized power 0 0.00 79.8 0.45 188 0.24 102.7 0.58 398 0.51 129.2 0.73 590 0.76 154.5 0.87 775Bep traffic 1.00 177.2 Bep HP 1.00 960 1.24 198.7 1.12

A third order polynomial power equation was derived using coefficients from the normalized power versus flow curve. Corrections are made in the power equation for speed and hydraulic efficiency.

The coefficients a, b and c of the normalized power versus flow curve define the shape of the normalized curve as follows:

0＝[(P _{BEP CORR} (a))/((Q _BEP ) ³ (η _{HBEP_CORR} ))](Q _ACT ) ³ +[((N _ACT )(P _{BEP CORR} )(b))/((N _Rated )(Q _BEP ) ² (η _{HBEP_CORR} ))](Q _ACT ) ² +[((N _ACT ) ² (P _{BEP CORR} )(c))/((N _Rated ) ² (Q _BEP )(η _{HBEP_CORR} )) ](Q _ACT )+(P _{SO_N} -(P _ACT /SG)),

in:

P _{BEP CORR} = Corrected pump power at BEP as determined from the tuned power curve at rated speed,

Q _BEP = Pump flow at BEP at rated speed,

所公布的值通常在0.7-0.95的范围内，η _{HBEP_CORR} = hydraulic efficiency correction,

Published values are usually in the range of 0.7-0.95,

N _ACT = actual operating speed,

N _Rated = rated speed,

P _{SO_N} = pump shutdown power at actual operating speed (determined from tuned power curve),

P _ACT = actual pump power,

SG = specific gravity, and

Q _ACT = Calculated actual flow rate at the current operating speed.

It should also be noted that for some embodiments, such as small hp pumps for liquids with a specific gravity other than 1.0, to improve accuracy, the contribution of P _ACT to mechanical losses (such as seals) in the power equation above can be adjusted as follows and bearings) to compensate:

P _{ACT CORR} = [((P _ACT -(Mech Loss x N _ACT /N _Rated ))/SG)+(Mech Loss x N _ACT /N _Rated )]

Also note again that for some embodiments such as sealless pumps, the eddy current loss estimate must be subtracted from the actual power reading in the power equation above.

Then, determine the complex roots in order to solve third order polynomials using Muller's method or other equivalent methods. The calculated actual flow is then determined for the specific operating point. Figure 8 shows a comparison of calculated power versus flow plotted for a third order polynomial power equation with actual flow data obtained from flow meter readings.

Since pump wear will affect pump power requirements, reducing flow accuracy, the power calculations can periodically be compensated for by performing another calibration as shown in step A.

other possible applications

Other possible applications include at least those listed below:

Pump Load Monitoring: Pump load monitoring depends on accurate modeling of pump power curves to identify minimum flow and shut-off conditions. While most load monitoring only monitors power at one speed, this logic provides more accurate load monitoring for variable speed operation.

Sensorless Flow Calculation: Sensorless flow estimation depends on accurate power curves to estimate pump flow. Using basic cutting laws may compromise the accuracy of the flow rate as the speed is reduced. This is especially true for small pumps where losses such as seals and bearings become more prominent and cannot be factored according to the cutting laws.

Pump Protection Algorithm: Sensorless flow measurement gives a reliable indication of operating conditions, whether operating at overload (too high flow), below minimum pump flow (too low flow), or shutting down Operate under the conditions of the relief valve.

Scope of the invention

It should be understood that any feature, characteristic, substitution or modification described herein for a particular embodiment can also be applied to or used for any other embodiment described herein or in conjunction with those embodiments, unless otherwise stated herein. combined. Furthermore, the figures are not drawn to scale here.

While the present invention has been described with respect to exemplary embodiments thereof, the foregoing and various other additions and omissions can be made in the exemplary embodiments without departing from the spirit and scope of the present invention.

Claims (54)

1. A method of determining pump flow in a centrifugal pump, centrifugal agitator, centrifugal blower, or centrifugal compressor, comprising:

creating a calibrated power curve for a valve closed condition at a number of rotational speeds by incrementing the rotational speed of the pump from a minimum rotational speed to a maximum rotational speed while operating the pump with the bleed valve closed, and collecting rotational speed and power data at the number of rotational speeds;

calculating a coefficient from a power versus flow curve as a function of a power ratio of the pump, wherein the power ratio of the pump is the power at a shut-down condition divided by the power at the optimum efficiency point at the maximum rotational speed corrected for the difference between the actual power and the published power; and

a polynomial power equation is solved for the flow at the current operating point based on the coefficients of the power versus flow curve.

2. The method of claim 1, wherein the power data for the valve closure is corrected to a specific gravity equal to 1.

3. The method of claim 1, wherein the method further compensates for mechanical losses, including seal and bearing losses, in the measured valve closed power reading based on the determination of closing power for a low power pump applied to a liquid having a specific gravity other than 1.0:

P_{SO_N}＝[(P_{Meas_N}-(Mech Loss x N_ACT/N_Rated))/SG]+(Mech Loss xN_ACT/N_Rated)，

wherein

The SG is the specific gravity,

P_{SO_N}is the off power at any rotational speed,

P_{Meas_N}is the measured off power at any rotational speed,

N_ACTis the actual operating rotational speed of the motor,

N_Ratedis the rated speed.

4. The method of claim 1, wherein the method comprises: for sealless pumps, the eddy current loss estimate is subtracted from the power reading of the actual valve closure.

5. The method of claim 1, wherein the method further comprises: based on the determination of the shut-down power at a rotational speed different from 100%, for the pump with the higher power, the heating of the liquid acted on by the pump is minimized and the power at 100% of the rotational speed is calculated:

P_{SO_100％}＝(N_100％/N_60％)^KSO x P_{SO_60％}，

wherein the KSO is the turn-off index,

P_{SO_100％}is the off power at 100% of the rated speed of the motor,

N_100％the rotation speed of 100 percent of the rated rotation speed of the motor,

N_60％is the rotation speed of 60 percent of the rated rotation speed of the motor,

P_{SO_60％}is the off power at 60% of the rated motor speed.

6. The method of claim 5, wherein the closing index value is 3.0.

7. The method of claim 1, wherein the method further comprises: the power of the valve closure at any speed is determined based on the determination of the closing power depending on the speed of the pump using a cubic interpolation method:

A＝(P_{SO_30％})/(N_30％)，

B＝(P_{SO_60％}-P_{SO_30％})/(N_60％-N_30％)，

C＝(B-A)/(N_60％-N_30％)，

D＝(P_{SO_100％}-P_{SO_60％})/(N_100％-N_60％)，

E＝(D-B)/((N_100％-N_30％) And an

F＝(E-C)/(N_100％) (ii) a And

wherein the turn-off power at any speed is calculated as follows:

P_{SO_N}＝A(N_ACT)+C(N_ACT)(N_ACT-N_30％)+F(N_ACT)(N_ACT-N_30％)(N_ACT-N_60％)，

wherein:

P_{SO_30％}＝P_{Meas_30％}the/SG is a measurement corrected to 1 by specific gravity at 30% of the rated speed of the motorThe power of the switch-off of (c),

P_{SO_60％}＝P_{Meas_60％}SG is the measured closing power at 60% of the rated motor speed, corrected by a specific gravity of 1, and

P_{SO_00％}＝P_{Meas_100％}the/SG is the measured closing power at 100% of the rated motor speed corrected by the specific gravity of 1,

the SG is the specific gravity,

P_{SO_N}is the off power at any rotational speed,

N_ACTis the actual operating rotational speed of the motor,

P_{SO_30％}is the turn-off power at 30% of the rated speed of the motor,

P_{SO_60％}is the off power at 60% of the rated speed of the motor,

P_{SO_100％}is the off power at 100% of the rated speed of the motor,

N_30％is the rotation speed of 30 percent of the rated rotation speed of the motor,

N_60％is the rotation speed of 60 percent of the rated rotation speed of the motor,

N_100％is the rotation speed of 100 percent of the rated rotation speed of the motor.

8. The method of claim 1, wherein the method further comprises: correcting the published power at the optimum efficiency point at rated speed based on actual valve closed power data.

9. The method of claim 8, wherein the method further comprises: correcting the published power based on the best efficiency point corrected according to:

$P_{\mathrm{BEP}\_\mathrm{corr}}=(P_{{\mathrm{SO}}_{100\%}}-P_{\mathrm{SO}})+P_{\mathrm{BEP}},$

wherein:

the BEP represents the point of best efficiency,

P_{BEP_corr}the corrected pump power at the BEP,

P_sothe pump power at 100% speed is off from the published curve,

P_BEPpump power at BEP at 100% speed from the published curve, and

10. the method of claim 1, wherein the method further comprises: the power ratio of the pump is determined by:

P_ratio＝P_{shutoff100％}/P_{BEP_corr}

wherein:

P_ratioas to the power ratio of the pump,

P_{shutoff100％}as the turn-off power at the rated speed,

$P_{\mathrm{BEP}\_\mathrm{corr}}=(P_{{\mathrm{SO}}_{100\%}}-P_{\mathrm{SO}})+P_{\mathrm{BEP}},$

P_sothe pump power at 100% speed is off from the published curve,

P_BEPpump power at 100% speed at best efficiency point BEP from the published curves, an

11. The method of claim 1, wherein the polynomial power equation is derived using coefficients from a normalized power versus flow curve.

12. The method of claim 11, wherein the method further comprises: compensating for mechanical losses including losses of seals and bearings for the accuracy of low power pumps for liquids with specific gravities other than 1.0 based on correcting for actual power in the polynomial power equation:

P_{ACT CORR}＝[((P_ACT-(Mech Loss x N_ACT/N_Rated))/SG)+(Mech Loss xN_ACT/N_Rated)]，

wherein,

the SG is the specific gravity,

P_{ACT CORR}the corrected actual pump power is then,

P_ACTis the actual pump power that is being pumped,

N_ACTis the actual operating rotational speed of the motor,

N_Ratedis the rated speed.

13. The method of claim 11, wherein the method further comprises: for sealless pumps, an eddy current loss estimate is subtracted from the actual power reading within the polynomial power equation.

14. The method of claim 11, wherein the method further comprises: correcting the rotation speed, hydraulic efficiency and specific gravity in the polynomial power equation.

15. The method of claim 14, wherein the method further comprises: a complex root is determined to solve the polynomial power equation using the Muller method or some other suitable method.

16. The method of claim 15, wherein the method further comprises: the calculated actual flow rate is determined for a particular operating point.

17. The method of claim 1, wherein the method further comprises: the method is performed on a variable frequency drive VFD or a programmable logic controller PLC.

18. The method of claim 1, wherein the method further comprises: the determined flow value is used as an input to a controller including a proportional-integral-derivative PID controller to control the flow without the need for a flow meter or other external measurement instrument.

19. A controller for determining a pump flow rate in a centrifugal pump, centrifugal agitator, centrifugal blower or centrifugal compressor, comprising modules:

a module configured to create a calibrated power curve for a valve closed condition at a number of rotational speeds by incrementing a rotational speed of the pump from a minimum rotational speed to a maximum rotational speed while operating the pump with the bleed valve closed, and collecting rotational speed and power data at the number of rotational speeds;

a module configured to calculate a coefficient from a power versus flow curve as a function of a power ratio of a pump, wherein the power ratio of the pump is the power at a shut-down condition divided by the power at a maximum speed corrected for the difference between actual power and published power at an optimum efficiency point; and

a module configured to solve a polynomial power equation for flow at a current operating point based on coefficients of a power versus flow curve.

20. The controller of claim 19, wherein the module is configured to correct the power data for the valve closure by a specific gravity equal to 1.

21. The controller of claim 19, wherein the module is configured to compensate for mechanical losses, including seal and bearing losses, in the measured valve closed power reading based on the determination of closed power for a low power pump applied to a liquid having a specific gravity other than 1.0:

P_{SO_N}＝[(P_{Meas_N}-(Mech Loss x N_ACT/N_Rated))/SG]+(Mech Loss xN_ACT/N_Rated)，

wherein

The SG is the specific gravity,

P_{SO_N}in other words the power is switched off at any rotational speed,

P_{Meas_N}is the measured off power at any rotational speed,

N_ACTis the actual operating rotational speed of the motor,

N_Ratedis the rated speed.

22. The controller of claim 19, wherein the module is configured to subtract an eddy current loss estimate from a power reading of actual valve closure for a sealless pump.

23. The controller of claim 19, wherein the module is configured to minimize heating of the liquid acted on by the pump for a higher power pump and calculate the power at 100% speed based on a determination of the power off at a speed other than 100% speed:

P_{SO_100％}＝(N_100％/N_60％)^KSO x P_{SO_60％}，

wherein the KSO is the turn-off index,

P_{SO_100％}the power off at 100% of the rated speed of the motor,

N_100％is the speed at 100% of the rated speed of the motor,

N_60％is the speed at 60% of the rated speed of the motor,

P_{SO_60％}is the off power at 60% of the rated motor speed.

24. A controller according to claim 23, wherein the closing index value is 3.0.

25. The controller of claim 19, wherein the module is configured to determine the power at which the valve closes at any speed based on a determination of the closing power that depends on the speed of the pump using a cubic interpolation method:

A＝(P_{SO_30％})/(N_30％)，

B＝(P_{SO_60％}-P_{SO_30％})/(N_60％-N_30％)，

C＝(B-A)/(N_60％-N_30％)，

D＝(P_{SO_100％}-P_{SO_60％})/(N_100％-N_60％)，

E＝(D-B)/(N_100％-N_30％) And an

F＝(E-C)/(N_100％) (ii) a And

wherein the turn-off power at any rotational speed is calculated as follows:

P_{SO_N}＝A(N_ACT)+C(N_ACT)(N_ACT-N_30％)+F(N_ACT)(N_ACT-N_30％)(N_ACT-N_60％)，

wherein:

P_{SO_30％}＝P_{Meas_30％}a/SG is as followsSpecific gravity 1 corrected shut-down power measured at 30% of the rated motor speed,

P_{SO_60％}＝P_{Meas_60％}SG is the measured closing power at 60% of the rated motor speed, corrected by a specific gravity of 1, and

P_{SO_100％}＝P_{Meas_100％}the/SG is the measured closing power at 100% of the rated motor speed corrected by the specific gravity of 1,

the SG is the specific gravity,

P_{SO_N}is the off power at any rotational speed,

N_ACTis the actual operating rotational speed of the motor,

P_{SO_30％}is the turn-off power at 30% of the rated speed of the motor,

P_{SO_60％}is the off power at 60% of the rated speed of the motor,

P_{SO_100％}is the off power at 100% of the rated speed of the motor,

N_30％is the rotation speed of 30 percent of the rated rotation speed of the motor,

N_60％is the rotation speed of 60 percent of the rated rotation speed of the motor,

N_100％is the rotation speed of 100 percent of the rated rotation speed of the motor.

26. The controller of claim 19, wherein the module is configured to correct the published power at the optimal efficiency point at a rated speed based on power data of actual valve closure.

27. The controller of claim 26, wherein the module is configured to correct the published power based on the best efficiency point corrected according to:

$P_{\mathrm{BEP}\_\mathrm{corr}}=(P_{{\mathrm{SO}}_{100\%}}-P_{\mathrm{SO}})+P_{\mathrm{BEP}},$

wherein:

the BEP is the point of best efficiency,

P_{BEP_corr}corrected pump power at BEP

P_soThe pump power at 100% speed is off from the published curve,

P_BEPpump power at BEP at 100% speed from the published curve, and

28. the controller of claim 19, wherein the module is configured to determine the power ratio of the pump by:

P_ratio＝P_{shutoff100％}/P_{BEP_corr}

wherein:

P_ratioas to the power ratio of the pump,

P_{shutoff100％}as the turn-off power at the rated speed,

$P_{\mathrm{BEP}\_\mathrm{corr}}=(P_{{\mathrm{SO}}_{100\%}}-P_{\mathrm{SO}})+P_{\mathrm{BEP}},$

P_sothe pump power at 100% speed is off from the published curve,

P_BEPpump power at 100% speed at best efficiency point BEP from the published curves, an

29. The controller of claim 19, wherein the power equation is a polynomial power equation derived using coefficients from a normalized power versus flow curve.

30. The controller of claim 29, wherein the module is configured to compensate for mechanical losses including seal and bearing losses for the accuracy of a low power pump for liquids with specific gravities other than 1.0 based on correcting for actual power in the polynomial power equation:

P_{ACT CORR}＝[((P_ACT-(Mech Loss x N_ACT/N_Rated))/SG)+(Mech Loss xN_ACT/N_Rated)]，

wherein,

the SG is the specific gravity,

P_{ACT CORR}the corrected actual pump power is then,

P_ACTis the actual pump power that is being pumped,

N_ACTis the actual operating rotational speed of the motor,

N_Ratedis the rated speed.

31. The controller of claim 29, wherein the module is configured to subtract an eddy current loss estimate from the actual power reading in the polynomial power equation for a sealless pump.

32. The controller of claim 29, wherein the module is configured to correct for rotational speed, hydraulic efficiency, and specific gravity within the polynomial power equation.

33. A controller as recited in claim 32, wherein the module is configured to determine a complex root to solve the polynomial power equation using a Muller method or some other suitable method.

34. The controller of claim 33, wherein the module is configured to determine the calculated actual flow rate for a particular operating point.

35. The controller of claim 19, wherein the controller comprises or forms part of a variable frequency drive VFD or a programmable logic controller PLC.

36. The controller of claim 19, wherein the module is configured to use the determined flow value as an input to a controller comprising a proportional-integral-derivative PID controller to control flow without requiring a flow meter or other external measurement instrument.

37. A system having a controller for determining pump flow rate within a centrifugal pump, centrifugal agitator, centrifugal blower, or centrifugal compressor, the controller comprising a module:

a module configured to create a calibrated power curve for a valve closed condition at a number of rotational speeds by incrementing a rotational speed of the pump from a minimum rotational speed to a maximum rotational speed while operating the pump with the bleed valve closed, and collecting rotational speed and power data at the number of rotational speeds;

a module configured to calculate a coefficient from a power versus flow curve as a function of a power ratio of a pump, wherein the power ratio of the pump is the power at a shut-down condition divided by the power at a maximum speed corrected for the difference between actual power and published power at an optimum efficiency point; and

a module configured to solve a polynomial power equation for flow at a current operating point based on coefficients of a power versus flow curve.

38. The pump system of claim 37, wherein the module is configured to correct the power data for the valve closure by a specific gravity equal to 1.

39. The pump system of claim 37, wherein the module is configured to compensate for mechanical losses, including seal and bearing losses, in measured valve closed power readings based on the determination of closed power for low power pumps applied to liquids having a specific gravity other than 1.0:

P_{SO_N}＝[(P_{Meas_N}-(Mech Loss x N_ACT/N_Rated))/SG]+(Mech Loss xN_ACT/N_Rated)，

wherein

The SG is the specific gravity,

P_{SO_N}to the power off at any rotational speed,

P_{Meas_N}is the measured off power at any rotational speed,

N_ACTthe actual speed of rotation of the operation is,

N_Ratedrated speed of rotation.

40. The pump system of claim 37, wherein the module is configured to subtract an eddy current loss estimate from a power reading of actual valve closure for a sealless pump.

41. The pump system of claim 37, wherein the module is configured to minimize heating of liquid acted on by the pump for higher power pumps and calculate power at 100% speed based on a determination of off power at speeds other than 100%:

P_{SO_100％}＝(N_100％/N_60％)^KSO x P_{SO_60％}，

wherein KSO is the shutdown index

P_{SO_100％}The power off at 100% of the rated speed of the motor,

N_100％is the rotation speed of 100 percent of the rated rotation speed of the motor,

N_60％is the rotation speed of 60 percent of the rated rotation speed of the motor,

P_{SO_60％}is the off power at 60% of the rated motor speed.

42. The pump system of claim 41, wherein the shutdown index value is 3.0.

43. The pump system of claim 37, wherein the module is configured to determine the power at which the valve closes at any rotational speed based on a determination of the closing power that depends on the rotational speed of the pump using a cubic interpolation method:

A＝(P_{SO_30％})/(N_30％)，

B＝(P_{SO_60％}-P_{SO_30％})/(N_60％-N_30％)，

C＝(B-A)/(N_60％-N_30％)，

D＝(P_{SO_100％}-P_{SO_60％})/(N_100％-N_60％)，

E＝(D-B)/(N_100％-N_30％) And an

F＝(E-C)/(N_100％) (ii) a And

wherein the turn-off power at any rotational speed is calculated as follows:

P_{SO_N}＝A(N_ACT)+C(N_ACT)(N_ACT-N_30％)+F(N_ACT)(N_ACT-N30％)(N_ACT-N60％)，

wherein:

P_{SO_30％}＝P_{Meas_30％}the/SG is the measured closing power at 30% of the rated motor speed corrected by the specific gravity of 1,

P_{SO_60％}＝P_{Meas_60％}SG is the measured closing power at 60% of the rated motor speed, corrected by a specific gravity of 1, and

P_{SO_100％}＝P_{Meas_100％}the/SG is the measured closing power at 100% of the rated motor speed corrected by the specific gravity of 1,

the SG is the specific gravity,

P_{SO_N}is the off power at any rotational speed,

N_ACTis the actual operating rotational speed of the motor,

P_{SO_30％}is the turn-off power at 30% of the rated speed of the motor,

P_{SO_60％}is the off power at 60% of the rated speed of the motor,

P_{SO_100％}is the off power at 100% of the rated speed of the motor,

N_30％is the rotation speed of 30 percent of the rated rotation speed of the motor,

N_60％is the rotation speed of 60 percent of the rated rotation speed of the motor,

N_100％is the rotation speed of 100 percent of the rated rotation speed of the motor.

44. The pump system of claim 37, wherein the module is configured to correct the published power at the optimal efficiency point at the rated speed based on power data of actual valve closure.

45. The pump system of claim 44, wherein the module is configured to correct the published power based on the best efficiency point corrected according to:

$P_{\mathrm{BEP}\_\mathrm{corr}}=(P_{{\mathrm{SO}}_{100\%}}-P_{\mathrm{SO}})+P_{\mathrm{BEP}},$

wherein:

the BEP is the point of best efficiency,

P_{BEP_corr}the corrected pump power at the BEP,

P_sothe pump power at 100% speed is off from the published curve,

P_BEPpump power at BEP at 100% speed from the published curve, and

46. the pump system of claim 37, wherein the module is configured to determine the power ratio of the pump by:

P_ratio＝P_{shutoff100％}/P_{BEP_corr}

wherein:

P_ratioas to the power ratio of the pump,

P_{shutoff100％}as the turn-off power at the rated speed,

$P_{\mathrm{BEP}\_\mathrm{corr}}=(P_{{\mathrm{SO}}_{100\%}}-P_{\mathrm{SO}})+P_{\mathrm{BEP}},$

P_sothe pump power at 100% speed is off from the published curve,

P_BEPpump power at 100% speed at best efficiency point BEP from the published curves, an

47. The pump system of claim 37, wherein the power equation is a polynomial power equation derived using coefficients from a normalized power versus flow curve.

48. The pump system of claim 47, wherein the module is configured to compensate for mechanical losses including seal and bearing losses for the accuracy of a low power pump for liquids with specific gravities other than 1.0 based on correcting for actual power in the polynomial power equation:

P_{ACT CORR}＝[((P_ACT-(Mech Loss x N_ACT/N_Rated))/SG)+(Mech Loss xN_ACT/N_Rated)]

wherein,

the SG is the specific gravity,

P_{ACT CORR}the corrected actual pump power is then,

P_ACTis the actual pump power that is being pumped,

N_ACTis the actual operating rotational speed of the motor,

N_Ratedis the rated speed.

49. The pump system of claim 47, wherein the module is configured to subtract an eddy current loss estimate from the actual power reading within the polynomial power equation for a sealless pump.

50. The pump system of claim 47, wherein the module is configured to correct for rotational speed, hydraulic efficiency, and specific gravity within the polynomial power equation.

51. The pump system of claim 50, wherein the module is configured to determine a complex root to solve the polynomial power equation using a Muller method or some other suitable method.

52. The pump system of claim 51, wherein the module is configured to determine a calculated actual flow rate for a particular operating point.

53. The pump system according to claim 37, wherein said controller comprises or forms part of a variable frequency drive VFD or a programmable logic controller PLC.

54. The pump system of claim 37, wherein the module is configured to use the determined flow value as an input to a controller comprising a proportional-integral-derivative PID controller to control flow without requiring a flow meter or other external measurement instrument.

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